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Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 Professors H. Ayhan and J. Dai Solutions to Homework 6 1. (a) The arrival rate, A to machine A is 12 jobs/hour. The service rate of machine A is 15 jobs/hour and the service rate of machine B is 30 jobs/hour. The utilization of machine A is A = 12 / 15 = 0 . 8 . Since A &lt; 1 the arrival rate to machine B is equal to A = 12 jobs/hour. Hence the utilization of machine B is A = 12 / 30 = 0 . 4 . (b) Since the utilizations of both machines are less than 1, the throughout is equal to the arrival rate to the system which is equal to 12 jobs/hour. (c) Using the Kingmans formula again E [ W q ] = c 2 a + c 2 s 2 - = . 8 3 = 0 . 2666 hrs = 16 mins (d) Using the Littles Law L = * W, where is the arrival rate and is equal to 12 jobs/hour and W = 30 mins = 0 . 5 hrs . Hence, L = 6 jobs. (e) If the arrival rate, A to machine A is 60 jobs/hour then the utilization of machine A is A = min { 60 / 15 , 1 } = 1 . Since A = 1 the arrival rate to machine B is equal to 15 jobs/hour. Hence the utilization of machine B is B = 15 / 30 = 0 . 5 ....
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